In this paper, we apply sparse identification to derive a low-complexity network model. The paper is inspired by the works in [1]} and [2]}. In these, a lean feedforward network is obtained by removing all edges (i.e., the connections between the neurons in the network) that have little or no influence on the quality of the fit. The network can be pruned by adding a sparsity-promoting regularization term to the cost function (or loss function) that is used to train the network; see lasso [3]} and sparse relaxed regularized regression [4]}, for instance. Alternatively, a sequential algorithm, such as stepwise regression [5]} or sequential thresholding [1]}, may be applied to remove all irrelevant edges in an iterative fashion. Other model-selection approaches are discussed in [7]} and [8]}. The sparse-identification methods in [1]} and [2]} rely on linear regression. Although they are relatively simple and fast enough to perform model identification in real time [11]}, [12]}, they rely on the limiting assumptions that the network model is linear in all its parameters, and that all system states are measured and their first-order time derivatives can be accurately approximated. This last condition commonly translates to the requirement of a sufficiently high sampling rate for all measurements in order to mitigate the negative influences of measurement noise by averaging over multiple samples. In [13]}, the computation of time derivatives of the states is based on Koopman theory. This technique can be applied to low-rate sampled data, but the requirement of a fixed sampling rate is often too restrictive to be applied to industrial data.
